0
Research Papers: Gas Turbines: Structures and Dynamics

# Rotating Flow and Heat Transfer in Cylindrical Cavities With Radial Inflow

[+] Author and Article Information
B. G. Vinod Kumar

e-mail: vb00052@surrey.ac.uk

John W. Chew

e-mail: j.chew@surrey.ac.uk

Nicholas J. Hills

e-mail: n.hills@surrey.ac.uk
Thermo-Fluid Systems UTC,
Faculty of Engineering and Physical Sciences,
University of Surrey,
Guildford, GU2 7XH, UK

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received July 24, 2012; final manuscript received August 20, 2012; published online February 21, 2013. Editor: Dilip R. Ballal.

J. Eng. Gas Turbines Power 135(3), 032502 (Feb 21, 2013) (12 pages) Paper No: GTP-12-1298; doi: 10.1115/1.4007826 History: Received July 24, 2012; Revised August 20, 2012

## Abstract

The design and optimization of an efficient internal air system of a gas turbine requires a thorough understanding of the flow and heat transfer in rotating disc cavities. The present study is devoted to the numerical modeling of flow and heat transfer in a cylindrical cavity with radial inflow and a comparison with the available experimental data. The simulations are carried out with axisymmetric and 3-D sector models for various inlet swirl and rotational Reynolds numbers up to 1.2 × 106. The pressure coefficients and Nusselt numbers are compared with the available experimental data and integral method solutions. Two popular eddy viscosity models, the Spalart–Allmaras and the k-$ɛ$, and a Reynolds stress model have been used. For cases with particularly strong vortex behavior the eddy viscosity models show some shortcomings, with the Spalart–Allmaras model giving slightly better results than the k-$ɛ$ model. Use of the Reynolds stress model improved the agreement with measurements for such cases. The integral method results are also found to agree well with the measurements.

<>

## References

Owen, J. M., and Wilson, M., 2001, “Some Current Research in Rotating-Disc Systems,” Ann. N.Y. Acad. Sci., 934, pp. 206–221. [PubMed]
Owen, J. M., Pincombe, J. R., and Rogers, R. H., 1985, “Source-Sink Flow Inside a Rotating Cavity,” J. Fluid Mech., 155, pp. 233–265.
Hide, R., 1968, “On Source-Sink Flows in a Rotating Fluid,” J. Fluid Mech., 32, pp. 737–764.
Wormley, D. N., 1969, “An Analytical Model for the Incompressible Flow in Short Vortex Chambers,” ASME J. Basic Eng., 91(2), pp. 264–272.
Chew, J. W., and Snell, R. J., 1988, “Prediction of the Pressure Distribution for Radial Inflow Between Co-Rotating Discs,” ASME GT and Aeroengine Congress, Amsterdam, June 5–9, ASME Paper No. 88-GT-61, p. 9.
Owen, J. M., and Rogers, R. H., 1995, “Flow and Heat Transfer in Rotating-Disc Systems, Volume 2: Rotating Cavities,” Mechanical Engineering Research Studies (Engineering Design Series), Research Studies Press, Somerset, UK/John Wiley & Sons Inc., New York.
Shevchuk, I. V., 2009, “Convective Heat and Mass Transfer in Rotating Disk Systems,” Lecture Notes in Applied and Computational Mechanics, Vol. 45, Springer, Heidelberg, Germany.
Childs, P. R. N., 2010, Rotating Flows, Butterworth-Heinemann, London.
Firouzian, M., Owen, J. M., Pincombe, J. R., and Rogers, R. H., 1985, “Flow and Heat Transfer in a Rotating Cavity With a Radial Inflow of Fluid—Part 1: The Flow Structure,” Int. J. Heat Fluid Flow, 6(4), pp. 228–234.
Firouzian, M., Owen, J. M., Pincombe, J. R., and Rogers, R. H., 1986, “Flow and Heat Transfer in a Rotating Cavity With a Radial Inflow of Fluid—Part 2: Velocity, Pressure and Heat Transfer Measurements,” Int. J. Heat Fluid Flow, 7(1), pp. 21–27.
Farthing, P. R., Chew, J. W., and Owen, J. M., 1991, “The Use of De-Swirl Nozzles to Reduce the Pressure Drop in a Rotating Cavity With a Radial Inflow,” ASME J. Turbomach., 113(1), pp. 106–114.
Chew, J. W., Farthing, P. R., Owen, J. M., and Stratford, B., 1989, “The Use of Fins to Reduce the Pressure Drop in a Rotating Cavity With a Radial Inflow,” ASME J. Turbomach., 111(3), pp. 349–356.
Volchkov, E. P., Semenov, S. V., and Terekov, V., 1991, “Heat Transfer and Shear Stress at the End Wall of a Vortex Chamber,” Exp. Therm. Fluid Sci., 4(5), pp. 546–557.
Farthing, P. R., 1989, “The Effect of Geometry on Flow and Heat Transfer in a Rotating Cavity,” D. Phil. thesis, University of Sussex, Brighton, UK.
Morse, A. P., 1988, “Numerical Prediction of Turbulent Flow in Rotating Cavities,” ASME J. Turbomach., 110, pp. 202–211.
Young, C., and Snowsill, G. D., 2003, “CFD Optimization of Cooling Air Offtake Passages Within Rotor Cavities,” ASME J. Turbomach., 125(2), pp. 380–386.
Gosman, A. D., Lockwood, F. C., and Loughhead, J. N., 1976, “Prediction of Recirculating, Swirling Flow in Rotating Disc Systems,” J. Mech. Eng. Sci., 18(3), pp. 142–148.
Chew, J. W., 1984, “Prediction of Flow in Rotating Disc Systems Using the k-ε Turbulence Model,” ASME Gas Turbine Conference, Amsterdam, June 4–7, ASME Paper No. 84-GT-229.
Dacles-Mariani, J., Zilliac, G. G., Chow, J. S., and Bradshaw, P., 1995, “Numerical/Experimental Study of a Wingtip Vortex in the Near Field,” AIAA J., 33(9), pp. 1561–1568.
Spalart, P. R., and Shur, M., 1997, “On the Sensitization of Turbulence Models to Rotation and Curvature,” Aerosp. Sci. Technol., 1(5), pp. 297–302.
Spalart, P. R., and Allmaras, S. R., 1994, “A One-Equation Turbulence Model for Aerodynamic Flows,” Rech. Aerosp., 1, pp. 5–21.
Torii, S., and Yang, W. J., 1995, “Numerical Prediction of Fully Developed Turbulent Swirling Flows in an Axially Rotating Pipe by Means of a Modified k-ε Turbulence Model,” Int. J. Numer. Methods Heat Fluid Flow, 5(2), pp. 175–183.
Smirnov, P. E., and Menter, F. R., 2009, “Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term,” ASME J. Turbomach., 131(4), p. 8.
Iacovides, H., and Toumpanakis, P., 1993, “Turbulence Modeling of Flows in Axisymmetric Rotor-Stator Systems,” Proceedings of the 5th International Symposium On Refined Flow Modeling Turbulence Measurements, Paris, September 7–10, p. 835.
Elena, L., and Schiestel, R., 1996, “Turbulence Modeling of Rotating Confined Flows,” Int. J. Heat Fluid Flow, 17, pp. 283–289.
Chen, J. C., and Lin, C. A., 1999, “Computations of Strongly Swirling Flows With Second-Moment Closures,” Int. J. Numer Methods Fluids, 30(5), pp. 493–508.
Virr, G. P., Chew, J. W., and Coupland, J., 1994, “Application of Computational Fluid Dynamics to Turbine Disc Cavities,” ASME J. Turbomach., 116(4), pp. 701–708.
Soghe, R. D., Innocenti, L., Andreini, A., and Poncet, S., 2010, “Numerical Benchmark of Turbulence Modeling in Gas Turbine Rotor-Stator System,” Proceedings of the ASME Turbo Expo 2010: Power for Land Sea and Air (GT2010), Glasgow, UK, June 14–18, ASME Paper No. GT2010-22627, pp. 771–783.
Launder, B. E., and Spalding, D. B., 1974, “The Numerical Computation of Turbulent Flows,” Comput. Methods Appl. Mech. Eng., 3(2), pp. 269–289.
Karman, von. Th., 1924, “Uber Laminare und Turbulente Reibung,” ZAMM, 1(4), pp. 233–252.
Chew, J. W., 1987, “Computation of Flow and Heat Transfer in Rotating Disc Systems,” Proceedings of the 2nd ASME-JSME Thermal Engineering Conference, Honolulu, HI, March 22–27, pp. 361–367.
Chew, J. W., and Rogers, R. H., 1988, “An Integral Method for the Calculation of Turbulent Forced Convection in a Rotating Cavity With Radial Outflow,” Int. J. Heat Fluid Flow, 9(1), pp. 37–48.
May, N. E., Chew, J. W., and James, P. W., 1994, “Calculation of Turbulent Flow for an Enclosed Rotating Cone,” ASME J. Turbomach., 116(3), pp. 548–554.
Moinier, P., 1999, “Algorithm Developments for an Unstructured Viscous Flow Solver,” D. Phil. thesis, University of Oxford, Oxford, UK.
FLUENT, 2006, “FLUENT 6.3 Documentation,” ANSYS, Inc., Canonsburg, PA.
Javiya, U., Chew, J. W., Hills, N. J., Zhou, L., Wilson, M., and Lock, G. D., 2011, “CFD Analysis of Flow and Heat Transfer in a Direct Transfer Preswirl System,” ASME J. Turbomach., 134(3), p. 031017.
Howard, J. H. G., Patankar, S. V., and Bordynuik, R. M., 1980, “Flow Prediction in Rotating Ducts Using Coriolis-Modified Turbulence Models,” ASME J. Fluids Eng., 102, pp. 456–461.
Shur, M. L., Strelets, M. K., and Travin, A. K., 2000, “Turbulence Modelling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction,” AIAA J., 38(5), pp. 784–792.
Iaccarino, G., Ooi, A., Reif, B. A. P., and Durbin, P., 1999, “RANS Simulations of Rotating Flows,” Annual Research Briefs, Center for Turbulence Research, Stanford, CA.
Poncet, S., Soghe, R. D., and Facchini, B., 2010, “RANS Modelling of Flow in Rotating Cavity System,” Fifth European Conference on Computational Fluid Dynamics (ECCOMAS CFD), Lisbon, Portugal, June 14–17.

## Figures

Fig. 1

Schematic of deswirled radial inflow in a rotating cavity

Fig. 2

Mesh used for test case S1

Fig. 4

Turbulent viscosity contours predicted by four turbulence models in test case S1

Fig. 3

Radial pressure distribution on the left end wall of the vortex chamber for test case S1 (Cw=2800, Reb=93,600). Wall functions: —, enhanced wall treatment: ---, and Wormley's [4] experiments: ○. Note that the vertical axis represents the ratio of the local gauge pressure to the inlet gauge pressure, as presented by Wormley [4].

Fig. 6

The tangential velocity profile at the axial midplane of the cavity for test case S2 (Reb=22,000, Cw=2360). Results using (a) eddy viscosity models in the Hydra and integral method, and (b) the RSM model in FLUENT.

Fig. 5

Mesh used for test case S2

Fig. 7

(a) Total temperature at the axial mid plane of the cavity, and (b) local Stanton number on the side wall opposite to the outlet vent at (Reb=200,000 and Cw=14,000) for test case S2

Fig. 8

The nondimensionalized tangential velocity profile at the axial midplane of the cavity for test case R1 (Reφ=3.45 × 105,Cw=1300). Results from turbulence models in (a) the Hydra and integral method, and (b) the FLUENT solver.

Fig. 9

3D geometry used for test case R2.1

Fig. 10

Nondimensional pressure distributions on the left hand disc for the test case R2.1 with Reφ=0.61 × 106, c=0.4, and λt=0.072. Results from the SA model: — the k-ɛ model: – – –, and Farthing's [14] experiments: o.

Fig. 11

Nondimensional pressure distributions on the left hand disc for the test case R2.1 with Reφ=0.61 × 106, c=0.0, and λt=0.120. Results from the SA model: —, the k-ɛ model,: – – –, and Farthing's [11,14] experiments: o.

Fig. 12

Variation of Cp,a with respect to Cw in the cavity in test case R2.2 (Reφ=0.61×106)

Fig. 13

Radial velocity contours on the radial-axial plane, midway between two successive nozzle exits in test case R2.2

Fig. 14

Local Nusselt number on the left hand disc for the test case R3 with Reφ=1.2×106, Cw=3500 and c=1.0. The SA model: —, the k-ɛ model: – – –, and Farthing's [14] experiments: o.

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections